The law of conservation of energy, which states that the amount of energy in a system is constant. For questions about Earth's environment, see the climate-science tag instead.

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Curious about this perpetuum concept

I know it's not possible to build a perpetual motion machine, but I still got this concept running in my mind. If you take a (longer)copper coil, and insert an axis through it(right-angled) with a ...
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0answers
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How to prove the energy of gravity in general relativity is non-local?

Every textbook in general relativity containing the energy of gravity all says that the energy of gravity is non-local and every energy-momemtum density received is pseudo-tensor, but "having not ...
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0answers
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Elementary thermodynamics problem? [on hold]

The maximum height reached by an aluminum rocket is $115\,\text{km}$. Upon reaching Earth, it is traveling with a speed of $1500\, \text{m}/\text{s}$. if 50% of the heat generated by friction with the ...
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5answers
6k views

Where does the extra kinetic energy come from in a gravitational slingshot?

I read in this answer in this site that the KE a free-falling ball acquires is not originated by the attracting body but that energy was actually stored in the ball when it had been lifted to the ...
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6answers
951 views
+300

If the universe is expanding, what is it expanding into?

If the universe is expanding, what is it expanding into? When the big bang happened where did it occur? When the big bang happened how did it occur? Where did the energy come from? Energy can not ...
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1answer
142 views

Why does electron move closer to the nucleus when it emits light and not vice-versa?

The book tells me that electrons move more close to the nucleus when emission occurs and it moves far away from the nucleus when absorption occurs: why it's not vice-vers? As I understand, the ...
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4answers
75 views

Virtual particles/quantum tunneling - conservation of energy?

I'm confused as to how the above phenomena can take place since arent they breaking the law of conservation of energy (even, if temporarily)?
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1answer
748 views

How is quantum tunneling possible?

How is quantum tunneling possible? According to quantum mechanics, each particle is represented by a probability density function. This function must be continuous, and therefore when we look at a ...
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3answers
402 views

Energy not conserved with accleration by a constant force

Suppose I have an object with mass $m$ in vacuum that I propel by applying a constant force, $F$, on it, with a rocket engine that I supply a constant amount of energy, $\frac{\delta ...
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3answers
344 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
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2answers
58 views

Calculating coefficient of friction

Consider a body attached to a horizontal spring and resting on a surface, inclined at an angle $\theta$ from the ground. The spring constant is $k$. Initially the spring was kept in its ...
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3answers
562 views

Conservation of Mathematical Constraints when deriving Energy and Momentum from $F=ma$

Background: Starting from $F = ma$, integrating with respect to time, and using basic calc, one can derive $\int Fdt = m (v_f - v_i)$ Starting from $F = ma$, integrating with respect to distance, ...
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1answer
91 views

How can a planet gravitationally capture objects?

I would expect that any asteroid or other object originating far away but passing near a planet would pick up speed and energy as it approaches, but unless it comes into contact with the atmosphere ...
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3answers
48 views

Why does the work done by an internal force differ from the work done by external force?

Let's consider the following situation. We put a body of mass $m$ at a distance $A$ from the center of Earth. We let the Earth attract the body and analyze the situation at a point $B$, closer to the ...
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5answers
667 views

How was the formula for kinetic energy found, and who found it?

My questions mostly concern the history of physics. Who found the formula for kinetic energy $E_k =\frac{1}{2}mv^{2}$ and how was this formula actually discovered? I've recently watched Leonard ...
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1answer
40 views

A pendulum's rope swings and strikes a peg [closed]

So I have this problem, as far as I can tell I solved it correctly, and it's not equal to any of my answer choices. The problem is: A rope of length $L$ is attached at one end to a ceiling and at ...
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1answer
77 views

If you spin a magnet in space, far from any magnet field, would it spin forever, being able to produce electricity forever?

This is of course a purely theoretical question and it would take energy to get the magnet moving in the first place but once it's moving in the vacuum of space, with no gravity or magnetic field ...
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3answers
296 views

Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
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2answers
352 views

How does escape velocity relate to energy and speed?

I have several confusions regarding escape velocity. I am sure I am missing something(s) obvious or maybe I am taught wrong. Lets say we throw an object of any mass at exactly escape velocity of ...
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1answer
234 views

As the universe expands, the wavelengths of photons are stretched, and energy is lost. What about electrons?

Will electrons, and other particles, also loose energy as they travel through the cosmos? They have wavelengths. Do they get "stretched"? My guess is that the EM force, somehow, counteracts this ...
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1answer
28 views

Gravitational Potential Energy to Kinetic Energy

When a yo-yo is released from a height $h$, the gravitational potential energy is converted to kinetic energy. However, the yo-yo obviously has less acceleration than $g$, $9.8\frac{m}{s}$. This means ...
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2answers
1k views

Finding max height of a mass launched by a spring?

I have the following problem on my homework. The actual problem has numbers, but I figure using symbolic notation will help me understand the concept in the long run. A block of mass $M$ is launched ...
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1answer
101 views

Sufficient conditions for the energy to be not conserved?

I'm almost embarrased to ask this question because I thought I was by now very confident with classical mechanics. Someone has stated that given a mechanical system with a Lagrangian $L$ s.t. ...
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2answers
97 views

Optimal speed for the water wheel

The hydroelectricity plants extract the potential energy of highly deployed massive object (water) as it falls down. Without turbine, all that energy would be converted into speed (kinetic energy) at ...
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2answers
62 views

Conservation of energy in a different frame of reference

Consider a rollercoaster that goes down a slope: At the higher level it has speed $v_0$, then it goes down a slope and at the end it has speed $v_0 + \Delta v$. The carriage is not powered and has ...
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3answers
491 views

Is it possible to deduce the conservation of angular momentum from the conservation of energy?

Is it possible to deduce the law of conservation of angular momentum from the law of conservation of energy? If possible, by what sense the conservation of angular momentum has the status of law, if ...
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10answers
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What happens to the energy when waves perfectly cancel each other?

What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be ...
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1answer
103 views

Poynting's Theorem simplified?

How can I apply Poynting's theorem to any system that has a magnetic field & electric field, to state conservation of energy? How does Poynting's theorem state conservation of energy in EM? I ...
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1answer
24 views

Understanding the energy transffered/used from a power source?

A source of power(from a generator,battery,etc...) is used to power a system of any kind. We can calculate the energy used via this formula $E$ = $IV$ x $t$ ? For example, a battery that is connected ...
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2answers
816 views

How did the inflaton field “add” energy to the universe?

How did inflation add energy to the universe? What mechanism did this occur by? In other words, where did that energy come from? Was it due to the quantum fluctuation (or that scalar field rolling ...
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2answers
91 views

Blueshift and increase in energy!

Imagine that there is a car and it is not moving but its headlights are on. There is a wall in front of the car but is very far away. Right now energy is being used only in switching on the ...
2
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1answer
40 views

Interference and energy question here

So Im reading this material on interference and I noted the following sentence : During the interference of the light of two coherent light sources,the intensity of the radiation changes ...
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2answers
73 views

Perspective and changes in kinetic energy

Say you have two planes flying next to each other at the same speed and one decides to pick up speed by burning a tank of rocket fuel. If someone on the ground wanted to know that plane's new speed ...
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1answer
41 views

Action Reaction Pairs and Work

Say that a ball is sitting in front of a compressed spring launcher. The spring is then released. The spring applies a force on the ball for a certain distance. This force is accompanied by an equal ...
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1answer
18 views

Given the spring constant & maximum kinetic energy; length of spring extension? [closed]

I need to understand the following question before i right my exam tomorrow. A body attached to a spring with spring constant 100 N/m executes simple harmonic motion. The maximum kinetiv energy of ...
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3answers
253 views

Two dimensional elastic collisions with varying angle of incident

If in an elastic collision I know all initial values and that mass for each object remains constant throughout the collision (but different from one another) how can I determine their final velocity ...
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2answers
76 views

Hamiltonian mechanics and conservation of energy?

Can anyone explain to me Hamiltonian mechanics relation to conservation of energy? I'm not very good at mathematics, and I know it's important into understanding Hamiltonian mechanics. However, can ...
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2answers
40 views

How to model energy loss in a rotating body?

I recently asked a question about modeling instability in a rotating rigid body. I now realize that I was mentally confounding two different effects: The "Dzhanibekov effect" in which a rigid ...
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2answers
72 views

What does $ {\bf F} = \frac{\mathrm{d}W}{\mathrm{d}{\bf x}}$ actually mean?

What does the formula $$ {\bf F} ~=~ \frac{\mathrm{d}W}{\mathrm{d}{\bf x}}$$ actually mean? Here $\mathrm{d}W$ is the work done in a small period, ${\bf F}$ is the force and $\mathrm{d}{\bf x}$ is a ...
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1answer
52 views

Black Hole mass increase from infalling body

When a body falls into a black hole, the black hole's mass increases. Does this mass increase depend only on the rest mass of the infalling object, or is it affected by the velocity of the infalling ...
3
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1answer
395 views

How to understand Feynman's reasoning about perpetual motion?

I'm studying Feynman's Lectures on Physics, and I'm not really understanding his reasoning here: Consider weight-lifting machines $\overline{}$ machines which have the property that they lift one ...
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1answer
51 views

Is the quantity $mv^{2}$ also conserved?

The following is my reasoning: Suppose $\vec{F}$ is a conservative force field. Then the total mechanical energy, $E$, of the isolated mechanical system is a conserved quantity which implies that ...
9
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2answers
481 views

When they say that the universe cooled after the big bang, where did the heat go?

Layman here, Stumbling through some physics stack posts and started reading the Wikipedia for the chronology of the big bang. In it, it states The very earliest universe was so hot, or energetic, ...
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3answers
71 views

Placing two similarly charged particles in space

Now, I will make a hypothetical situation. Assume that we place two similarly charged particles (lets take electrons) in space. Imagine that there is no other force acting on the particles except the ...
2
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1answer
76 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
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2answers
6k views

Perfect elastic collision and velocity transfer

So my teacher told me that when you have two identical balls in a perfectly elastic collision, the first ball A will collide with B and afterwards A will stop and B continue. Why is this? Doesn't ...
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4answers
300 views

Potential Energy Concept

Imagine a book that we lift it with a force that is exactly equal to the force of gravity so the forces cancel out and the book moves with a constant velocity. Consider the situation after the book ...
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1answer
49 views

Redshift of a reflected photon from a solar sail

Can someone help me understand my mistake here? I'm thinking of a photon travelling with momentum $p=h/\lambda$ which reflects off a solar sail of mass $m$ travelling with momentum $p_0$ in the same ...
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1answer
62 views

Finding direction of a ball after collision in cartesian coordinate system [closed]

In elastic collision of ball to wall along x axis m*Vix=m*Vfx as velocity of wall is 0 before and after collision thus Vix=Vfx ......eq(1) Kinetic Energy is conserved so m*Vi2 = m*Vf2 (Vix2 + ...
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3answers
599 views

What is the most efficient machine for translating gravitational potential energy of one mass into kinetic energy of a different mass?

As the question states, what is our current best machine for translating falling gravitational potential energy, such as a large weight, into launching a smaller projectile vertically? A lever? A ...